Partial-difference subtraction, lattice multiplication, partial quotient division, Egyptian multiplication.... To many parents these are foreign words, but to many elementary school students this is the new math. We are told that these alternatives are in the curriculum so that the student will have the freedom to choose the method he or she likes he best.
But parents don't give these same students the freedom to eat or buy anything they want or do anything they please, the rationale being that they do not yet have the knowledge or the maturity to make an intelligent choice.
Should mathematics be held to the same criteria? Are students made aware that partial quotient division gets very dicey when the quotent or the dividend is a decimal number? Are they cautioned that lattice multiplication is slow and cumbersome, requires special consideration of where to place the decimal point, and gives no insight into the multiplication process? Do they realize that the combination of lattice multiplication and partial quotient division can turn a long-division problem into a lengthy project? Should a parent be concerned when their child constructs a lattice to multiply two times eleven?
Many students find "conventional" division difficult to learn. Partial quotient division makes this operation somewhat easier, especially for those who do not multiply well. Are we saying that students that are being taught algebra, geometry, scientific notation and other complex subjects can't be taught "conventional" long division? Are we saying that students must learn the meaning of rarely-used words such as heptagon, reflex angle, nonconvex polygon, etc. but cannot be made to learn the multiplication table? And where does this lead? If a sixth grader can do algebra and geometry but not multiplication and division, should we omit basic arithmetic altogether and rely on the calculator?
It seems a bit ironic that while students are given the freedom to choose whatever multiplication or division method they like, they are required to learn other methods even if they do not like them. Thus a student who prefers and knows partial product or "conventional" multiplication well must also learn lattice multiplication even though it is much more cumbersome. And a student that knows "conventional" division well must also learn partial quotient division. Isn't this like forcing a right-handed person to learn to write left-handed?
On the other hand, it is laudable that mathematical concepts formerly introduced at the secondary school level are now available to fifth and sixth graders. But writers, lawyers, doctors, and many other professionals do not need to know algebra to succeed, ditto for mechanics, carpenters, electricians, nurses and the like. Is advanced math being forced onto everyone because of the current need for hi-tech personnel? If there were a shortage of musicians, would we force everyone to play a musical instrument regardless of their aptitude or desire? Perhaps the problem is that advanced math has been pushed into the fifth and sixth grade levels, but the separation of students according to aptitude and desire has not. In any case, the result seems to be much teacher and student frustration.
And so we ponder, what is the goal of education reform? Is it to raise the bar on what every graduate should know? Or, is it to educate each student to his or her fullest potential?